Expressivity of many-valued modal logics, coalgebraically

Abstract

We apply methods developed to study coalgebraic logic to investigate expressivity of many-valued modal logics which we consider as coalgebraic languages interpreted over set-coalgebras with many-valued valuations. The languages are based on many-valued predicate liftings. We provide a characterization theorem for a language generated by a set of such modalities to be expressive for bisimilarity: in addition to the usual condition on the set of predicate liftings being separating, we indicate a sufficient and sometimes also necessary condition on the algebra of truth values which guarantees expressivity. Thus, adapting results of Schr¨oder [16] concerning expressivity of boolean coalgebraic logics to many-valued setting, we generalize results of Metcalfe and Martí [13], concerning Hennessy-Milner property for many-valued modal logics based on ⧠ and ◇.